Given X = {x | x < 7}, Y = {x | x ≥ −2}, and Z = {x | x < −3}, write the union or intersection in set-builder notation. a.X∪Y b.X∩ Y c.X∪ Z d.X∩ Z e.Y∪Z f.Y∩ Z

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A: It can be solved by the set theory

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A: See solution below

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A:

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A:

Q: 4. In each case, sketch the closure of the set: (a) –n 0.

A: Note: Since you have posted multiple subparts we will solve only three subparts for you. If you want…

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A: Answer

Q: If R is the universal set, find: 1. Q ∩ R 2. Z ∩ I 3. N ∩ I

A: Since R is universal set.

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A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

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Q: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

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A:

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A: The solution is given as

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A:

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A: The Venn diagram for 2 sets can be drawn as follows.

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A: Suppose S is set having n elements and T is a set having m elements. That is n&gt;m More precisely,…

Q: 3. Given X = {x|x-2}, and Z = {x|x< -3}, write the union or intersection in set-builder notation. а.…

A: Given that, X=x| x&lt;7, Y=x| x≥-2 and Z=x| x&lt;-3 Since,  Set X represents all real numbers less…

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A:

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A:

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A:

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Q: Q3 ( Let A, B and C be sets. Show that (C – A)n (A – B) = 0, without using membership tables.

A:

Q: Use set builder notations to prove that:  (a) X ⊕ Y = (X ∪ Y ) − (X ∩ Y ),           (b)(Y −X) ∪ (Z…

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A: Here use definition of equivalent set

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A: B=C

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A:

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Q: Let A, B, C be sets. Simplify (A∪(B∩C))∪((Bc ∩Cc)∪C)c

A:

Q: Let A and B be sets. Then B - (B – A) AN B is equal to the above

A: Let A and B be sets  Let x∈B-B-A ⇔x∈B and x∉B-A ⇔x∈B∧x∉B∨x∈A⇔x∈B∧x∉B∨x∈B∧x∈A⇔x∈B∧x∈A⇔x∈A∩B ( since…

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A: Given: A⊂-B, |B| = |C| = 5 and | B∩C| = 4

Q: Let A and B be sets. Then B - (B - A) ANB is equal to the above Ā NB is equal to the above

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.